8 citations · 28 across the 9 of their papers we have counts for
13 papers
Fractional triangle decompositions in almost complete graphs
Vytautas Gruslys, Shoham Letzter
We prove that every -vertex graph with at least edges has a fractional triangle decomposition, for . This is a key ingredient in our proof, giv…
Monochromatic triangle packings in red-blue graphs
Vytautas Gruslys, Shoham Letzter
We prove that in every -edge-colouring of there is a collection of edge-disjoint monochromatic triangles, thus confirming a conjecture of Erdős. We also…
Lagrangians of Hypergraphs II: When colex is best
Vytautas Gruslys, Shoham Letzter, Natasha Morrison
A well-known conjecture of Frankl and Füredi from 1989 states that an initial segment of colex of has the largest Lagrangian of any -uniform hypergraph with hyperedges. We s…
Cycle partitions of regular graphs
Vytautas Gruslys, Shoham Letzter
Magnant and Martin conjectured that the vertex set of any -regular graph on vertices can be partitioned into paths (there exists a simple construction showin…
Hypergraph Lagrangians I: the Frankl-Füredi conjecture is false
Vytautas Gruslys, Shoham Letzter, Natasha Morrison
An old and well-known conjecture of Frankl and Füredi states that the Lagrangian of an -uniform hypergraph with edges is maximised by an initial segment of colex. In this pa…
Almost partitioning the hypercube into copies of a graph
Vytautas Gruslys, Shoham Letzter
Let be an induced subgraph of the hypercube , for some . We show that for some , the vertices of can be partitioned into induced copies of and a rem…